Convection currents are caused by an uneven temperature within something. Convection currents happen within the Earth's magma, water and air. It can happen in anything that is not solid and has parts that are cooler or warmer than other parts.
When something is cool, it sinks, and when it is hot, it rises. This is the essential driving force behind convection currents. Water in a pot that is heating toward boiling has a convection current that is easy to understand. The top of the water is exposed to the cooler air, and when it starts to bubble then it releases even more heat. The bottom of the water is heated by the stovetop. The cooler water on top sinks and is replaced by the warmer water, which then cools off due to exposure to air, which then repeats the process.
This simple example is easily scaled up to the large magma pockets beneath the crust of the Earth that drives plate tectonics, or to the oceans, where convection currents help to create the large-scale ocean currents that drive ships and marine life. There are also convection currents in the atmosphere, which help form both weather and clouds, as well as creating wind and major air currents similar to the ocean currents.